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 Electronic Communications in Probability > Vol. 9 (2004) > Paper 6 open journal systems 


Tree and Grid factors of General Point processes

Adam Timar, Indiana University


Abstract
We study isomorphism invariant point processes of R^d; whose groups of symmetries are almost surely trivial. We define a 1-ended, locally finite tree factor on the points of the process, that is, a mapping of the point configuration to a graph on it that is measurable and equivariant with the point process. This answers a question of Holroyd and Peres. The tree will be used to construct a factor isomorphic to Z^n. This perhaps surprising result (that any d and n works) solves a problem by Steve Evans. The construction, based on a connected clumping with 2^i vertices in each clump of the i'th partition, can be used to define various other factors.


Full text: PDF

Pages: 53-59

Published on: April 21, 2004
Bibliography
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  3. P. A. Ferrari, C. Landim, H. Thorisson. Poisson trees, succession lines and coalescing random walks. Preprint. Math. Review number not available.
  4. A. E. Holroyd, Y. Peres. Trees and matchings from point processes. Elect. Comm. in Probab. , 8 (2003), 17-27. Math. Review number not available.
















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Electronic Communications in Probability. ISSN: 1083-589X